7,271 research outputs found
On the Photorefractive Gunn Effect
We present and numerically solve a model of the photorefractive Gunn effect.
We find that high field domains can be triggered by phase-locked interference
fringes, as it has been recently predicted on the basis of linear stability
considerations. Since the Gunn effect is intrinsically nonlinear, we find that
such considerations give at best order-of-magnitude estimations of the
parameters critical to the photorefractive Gunn effect. The response of the
system is much more complex including multiple wave shedding from the injecting
contact, wave suppression and chaos with spatial structure.Comment: Revtex, 8 pag., 4 fig. (jpg), submit to Physical Review
Chaotic motion of space charge wavefronts in semiconductors under time-independent voltage bias
A standard drift-diffusion model of space charge wave propagation in
semiconductors has been studied numerically and analytically under dc voltage
bias. For sufficiently long samples, appropriate contact resistivity and
applied voltage - such that the sample is biased in a regime of negative
differential resistance - we find chaos in the propagation of nonlinear fronts
(charge monopoles of alternating sign) of electric field. The chaos is always
low-dimensional, but has a complex spatial structure; this behavior can be
interpreted using a finite dimensional asymptotic model in which the front
(charge monopole) positions and the electrical current are the only dynamical
variables.Comment: 12 pages, 8 figure
Bifurcation analysis and phase diagram of a spin-string model with buckled states
We analyze a one-dimensional spin-string model, in which string oscillators
are linearly coupled to their two nearest neighbors and to Ising spins
representing internal degrees of freedom. String-spin coupling induces a
long-range ferromagnetic interaction among spins that competes with a spin-spin
antiferromagnetic coupling. As a consequence, the complex phase diagram of the
system exhibits different flat rippled and buckled states, with first or second
order transition lines between states. The two-dimensional version of the model
has a similar phase diagram, which has been recently used to explain the
rippled to buckled transition observed in scanning tunnelling microscopy
experiments with suspended graphene sheets. Here we describe in detail the
phase diagram of the simpler one-dimensional model and phase stability using
bifurcation theory. This gives additional insight into the physical mechanisms
underlying the different phases and the behavior observed in experiments.Comment: 15 pages, 7 figure
Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer
Electron scattering on a thin layer where the potential depends
self-consistently on the wave function has been studied. When the amplitude of
the incident wave exceeds a certain threshold, a soliton-shaped brightening
(darkening) appears on the layer causing diffraction of the wave. Thus the
spontaneously formed transverse pattern can be viewed as a self-induced
nonlinear quantum screen. Attractive or repulsive nonlinearities result in
different phase shifts of the wave function on the screen, which give rise to
quite different diffraction patterns. Among others, the nonlinearity can cause
self-focusing of the incident wave into a ``beam'', splitting in two ``beams'',
single or double traces with suppressed reflection or transmission, etc.Comment: RevTex, 4 pages, epsf.sty to insert figures, to appear in Phys.Rev.
Nonequilibrium free energy, H theorem and self-sustained oscillations for Boltzmann-BGK descriptions of semiconductor superlattices
Semiconductor superlattices (SL) may be described by a Boltzmann-Poisson
kinetic equation with a Bhatnagar-Gross-Krook (BGK) collision term which
preserves charge, but not momentum or energy. Under appropriate boundary and
voltage bias conditions, these equations exhibit time-periodic oscillations of
the current caused by repeated nucleation and motion of charge dipole waves.
Despite this clear nonequilibrium behavior, if we `close' the system by
attaching insulated contacts to the superlattice and keeping its voltage bias
to zero volts, we can prove the H theorem, namely that a free energy
of the kinetic equations is a Lyapunov functional (, ). Numerical simulations confirm that the free energy decays to its
equilibrium value for a closed SL, whereas for an `open' SL under appropriate
dc voltage bias and contact conductivity oscillates in time with the
same frequency as the current self-sustained oscillations.Comment: 15 pages, 3 figures, minor revision of latex fil
Chaos in resonant-tunneling superlattices
Spatio-temporal chaos is predicted to occur in n-doped semiconductor
superlattices with sequential resonant tunneling as their main charge transport
mechanism. Under dc voltage bias, undamped time-dependent oscillations of the
current (due to the motion and recycling of electric field domain walls) have
been observed in recent experiments. Chaos is the result of forcing this
natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon
request from [email protected], to appear in Phys.Rev.
Two mini-band model for self-sustained oscillations of the current through resonant tunneling semiconductor superlattices
A two miniband model for electron transport in semiconductor superlattices
that includes scattering and interminiband tunnelling is proposed. The model is
formulated in terms of Wigner functions in a basis spanned by Pauli matrices,
includes electron-electron scattering in the Hartree approximation and modified
Bhatnagar-Gross-Krook collision tems. For strong applied fields, balance
equations for the electric field and the miniband populations are derived using
a Chapman-Enskog perturbation technique. These equations are then solved
numerically for a dc voltage biased superlattice. Results include
self-sustained current oscillations due to repeated nucleation of electric
field pulses at the injecting contact region and their motion towards the
collector. Numerical reconstruction of the Wigner functions shows that the
miniband with higher energy is empty during most of the oscillation period: it
becomes populated only when the local electric field (corresponding to the
passing pulse) is sufficiently large to trigger resonant tunneling.Comment: 26 pages, 3 figures, to appear in Phys. Rev.
Effects of disorder on the wave front depinning transition in spatially discrete systems
Pinning and depinning of wave fronts are ubiquitous features of spatially
discrete systems describing a host of phenomena in physics, biology, etc. A
large class of discrete systems is described by overdamped chains of nonlinear
oscillators with nearest-neighbor coupling and subject to random external
forces. The presence of weak randomness shrinks the pinning interval and it
changes the critical exponent of the wave front depinning transition from 1/2
to 3/2. This effect is derived by means of a recent asymptotic theory of the
depinning transition, extended to discrete drift-diffusion models of transport
in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.
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